Vortex-Pair Excitation near the Superconducting Transition of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$Ca${\mathrm{Cu}}_2$${\mathrm{O}}_8$ Crystals

The dissipation observed at the superconducting transition of the high-$T_c$ superconductor ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$Ca${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$ is explained quantitatively by the Kosterlitz-Thouless theory of vortex-antivortex pair excitations within the Cu${\mathrm{O}}_2$ planes. This conclusion is drawn from the observation of an exponential square-root singularity in the resistivity and a power-law dependence of the resistivity on magnetic field. The Kosterlitz-Thouless phase transition ($T_c=84.7\mathrm{}$ K) is at the $\rho =0\mathrm{}$ point, and the mean-field Ginzburg-Landau transition ($T_{c0\mathrm{}}=86.8\mathrm{}$ K) at ∼25% of the normal-state resistivity.